Problems _1-3. Application Problems about Radio active decay, Mixing Problem (rate in - rate out) and Newton's law of cooling. Problems within Image.

You may or may not need to use the following formulas/defmitions Q' = kQ Q' =aQ T' = k(TTm) Q' =rateinrate out 1) [1.5 pts] A certain radioactive material decays at a rate proportional to the amount present. The half-life of a radioactive decay substance is 5 days. If the initial mass is 8 grams, how much will be left in 3 days? 2) [1.5 pts] A 200 liter tank initially contains 60 kilograms of salt dissolved in 100 liters of water. Starting at to = 0, water that contains 2 kilograms of salt per liter is added to the tank at the rate of 4 liters/min and the resulting mixture is drained from the tank at 3 liters/min. Let Q(t) be the amount salt in the tank after 1' minutes. Write the differential equation for the amount of salt in the tank at any time t, t > 0, prior to overow. Include any initial conditions. Do not solve! 3) [2.5 pts] In honor of Pi Day (March 14th in case anyone forgot), a pie is removed from an oven at 210 F and is placed in a room where the temperature is 77F. After 40 minutes the temperature of the pie is 130F. If the pie cools according to Newton's law of cooling, what is the temperature of the pie after 1 hour? a) Write the differential equation for the temperature of the pie, TU), after 1' minutes. Include any initial conditions. b) Solve the differential equation in part a) and determine the temperature of the pie after 1 hour